
Differential ages of passively evolving galaxies: The Hubble parameter \(H(z)\)  can be expressed in the terms of the rate of change of cosmic time with the redshift, given by
\(H(z)= - \dfrac{1}{(1+z)} \dfrac{\Delta z}{\Delta t}.\) 
The change of cosmic time with redshift can be estimated from the ageing of the stellar population in the galaxies. However, one needs to be extremely careful in selecting the galaxies while calculating the \(H(z)\)  values using this method. In young evolving galaxies, the stars are being born continuously and the emission spectra will be dominated by the young stellar population. Hence to estimate accurately the differential ageing of the universe, passively evolving red galaxies are used as their light is mostly dominated by the old stellar population [1]}. To find \(H(z)\)  at a given redshift, the ages of the early type passively evolving galaxies with similar metallicity and very small redshift interval is calculated. The redshift difference \(\Delta z\)  between two galaxies can be measured by using spectroscopic observations. For the estimation of \(\Delta t\) , [2]} suggested the use of a direct spectroscopic observable (the 4000 Å break) which is known to be linearly related to the age of the stellar population of a galaxy at fixed metallicity. As the measure of \(H(z)\)  is estimated purely by using spectroscopic observations, it is cosmological model-independent and has proved to be a strong probe to constrain cosmological models and assumptions. This method of calculating \(H(z)\)  is usually known as the “Cosmic Chronometers” and data points are generally referred to as CC \(H(z)\) . Out of 51 \(H(z)\)  measurements, 31 points have been estimated using this differential ages of passively evolving galaxies technique [3]}, [4]}, [5]}, [2]}, [7]}, [8]}.
<FIGURE>
